具有密度依赖的Monod-Haldane反应项捕食模型的动态分歧和跃迁

Dynamic Bifurcation and Transition of Predator-Prey Model with Density-Dependent Monod-Haldane Response

本文研究具有密度依赖的Monod-Haldane反应项捕食模型在齐次Dirichlet边界条件下的动态分歧和跃迁.利用中心流形约化以及动态分歧理论,在两种不同情形下分别得到跃迁类型及其判据,给出吸引域的刻画,补充和完善相关文献中的已有结果.最后通过数值模拟验证理论分析的正确性并给出生物学解释.

In this paper, the dynamic bifurcation and the transition of predator-prey model with density-dependent Monod-Haldane response under homogeneous Dirichlet boundary conditions are investigated. With the center manifold reduction and the dynamic bifurcation theory, the types and the criterion of transitions are both derived in two different cases respectively. The descriptions of the basin of attractor are given, which supplements the existing results in the relevant literatures. At last, the correctness of the theoretical analysis is verified by the numerical simulations and the biological explanations are given.